What is a multiplet?

Could someone please explain what a multiplet is? I know that this has to do with the representation theory of Lie Algebras and I know that elementary particles somehow group themselves into multiplets, but that's about as far as my knowledge goes. A good book or review article explaining multiplets and representation theory in general would be extremely helpful.

If you did some quantum mechanics, then you might recall that the angular momentum states group themselves into multiplets labeled by j. Same thing is going on, except that for groups other than SU(2), you get more labels.